Rotational Mechanical Converter (MA)

Interface between humid air and mechanical rotating networks.

blockType: AcausalFoundation.MoistAir.Elements.RotationalMechanicalConverter

Path in the library:

/Physical Modeling/Fundamental/Moist Air/Elements/Rotational Mechanical Converter (MA)

Description

The Rotational Mechanical Converter (MA) unit represents the interface between the humid air network and the mechanical rotational network. The unit converts moist air pressure into mechanical torque and vice versa. It can be used as a basis for rotary actuators.

The volume of moist air in the converter changes during operation. The pressure and temperature change according to the compressibility and heat capacity of the moist air volume. Liquid water condenses out of the moist air volume when it reaches saturation.

The Mechanical orientation parameter determines whether an increase in humid air volume causes the R port to rotate positively or negatively with respect to the C port.

Port A is the wet air port corresponding to the inverter input. Ports R and C are the mechanical rotation ports corresponding to the shaft and housing, respectively.

Sub-line indices

- properties of dry air, water vapour and impure moist air, respectively.
- Water vapour at saturation.
- corresponding port.
- properties of the internal volume of moist air.

Characteristics of the modelled system

- mass flow rate.
- energy flow rate.
- heat flow rate.
- pressure.
- density.
- universal gas constant.
- volume of moist air inside the converter.
- specific heat capacity at constant volume.
- specific enthalpy.
- specific internal energy.
- mass fraction ( - specific humidity, which is otherwise known as the mass fraction of water vapour).
- mole fraction.
- relative humidity.
- humidity coefficient.
- temperature.
- time.

Then the net wet air flow rates in the vessel are:

Where:

- condensation rate.
- is the rate of condensate energy loss.
- rate of energy addition from moisture sources and impurity gases.
and are mass flow rates of water and air through the S port.

The values and are determined by the moisture and impurity gas sources connected to the S port of the inverter.

If the port is not used, the terms of the equation with the subscript corresponding to the port name are .

Water vapour mass conservation relates the mass flow rate of water vapour to the dynamics of the humidity level in the internal volume of humid air:

Similarly, the conservation of admixture gas mass relates the mass flow rate of admixture gas to the dynamics of the level of admixture gas in the internal volume of humid air:

Conservation of mixture mass relates the mass flow rate of the mixture to the dynamics of pressure, temperature, and mass fractions of the internal volume of moist air:

where is the rate of change of the transducer volume.

Finally, the law of conservation of energy relates the rate of energy flow to the dynamics of pressure, temperature and mass fractions of the internal volume of moist air:

The equation of state relates the density of the mixture to pressure and temperature:

The universal gas constant of the mixture is equal to:

The volume of the converter depends on the shaft rotation:

Where:

- is the fluid volume at which the shaft angle of rotation is 0.
- is the volume displacement of the shaft.
- shaft rotation angle.
- is the mechanical orientation factor. If Mechanical orientation is set to Pressure at A causes positive rotation of R relative to C, then , otherwise .

The shaft rotation is zero if the volume of moist air inside the converter is equal to . Then, depending on the value of the Mechanical orientation parameter, the following is true:

If it is set to Pressure at A causes positive rotation of R relative to C, the interface rotation increases when the wet air volume increases compared to the dead volume.
If it is set to Pressure at A causes negative rotation of R relative to C, the rotation of the interface decreases when the volume of moist air increases compared to the dead volume.

Equation describing the torque equilibrium at the inverter:

where:

- torque from port R to port C.
- atmospheric pressure.

The gas and thermal resistances in the converter are not modelled:

When the air reaches saturation, condensation can occur. The specific humidity at saturation is:

where:

- is the relative humidity of the air at saturation (typically 1).
- water vapour saturation pressure estimated at .

The condensation rate is:

where:

- Condensation time constant parameter value.

Condensate is subtracted from the volume of moist air as shown in the conservation equations. The energy associated with the condensate is equal to:

where is the specific enthalpy of vapour formation, estimated at .

Other quantities of moisture and impurity gas are related as follows:

Assumptions and limitations

The walls of the converter are perfectly rigid.
The gas resistance between the inlet and the interior of the transducer is negligible.
The thermal resistance between the H port and the wet air volume is not modelled.
The movable interface operates without losses.
The unit does not model mechanical effects such as hard stopping, friction and inertia.

Ports

Output

W - condensation rate, kg/sec
scalar

Output port that measures the condensation rate in the inverter.

F - vector signal containing pressure, temperature, humidity and impurity gas level data
vector

Output port that outputs a vector signal. The vector contains the results of pressure (Pa), temperature (K), humidity and impurity gas level measurements inside the component.

Non-directional

A - humid air input
`humid air

Wet air port, corresponds to the inverter input.

H is the temperature inside the transmitter
heat

Heat port related to the temperature of the moist air mixture inside the converter.

R - shaft
`rotational mechanics

Mechanical progressive port, corresponds to a shaft.

C - housing
translational mechanics

Mechanical progressive port, corresponds to the inverter housing.

S - adding or removing moisture and impurity gases
`moisture and gas impurity'.

Connect this port to the S port of a S block from the Moisture & Trace Gas Sources library to add or remove moisture and impurity gases.

Dependencies

This port is visible only when Moisture and trace gas source is set to `Controlled'.

Parameters

Mechanical orientation - select the orientation of the transducer
Pressure at A causes positive rotation of R relative to C (by default) | `Pressure at A causes negative rotation of R relative to C `

Select the shaft movement relative to the humid air volume inside the converter:

Pressure at A causes positive rotation of R relative to C - An increase in the humid air volume causes positive rotation of port R relative to port C.
Pressure at A causes negative rotation of R relative to C - An increase in the volume of humid air causes negative rotation of port R relative to port C.

Initial interface rotation - rotational offset of port R relative to port C at the start of the simulation
0 (By default)

Rotational displacement of port R relative to port C at the beginning of the simulation. The value 0 corresponds to the initial volume of moist air equal to Dead volume.

Dependencies

Enabled if Interface rotation is set to Calculate from angular velocity of port R relative to port C..

If Mechanical orientation is Pressure at A causes positive rotation of R relative to C, the parameter value must be greater than or equal to 0.
If Mechanical orientation - Pressure at A causes negative rotation of R relative to C, the value of the parameter must be less than or equal to 0.

Interface volume displacement - volume of displaced moist air per unit revolution
0.01 m³/rad (by default).

Volume of displaced moist air per unit revolution of the shaft.

Dead volume - volume of moist air at shaft rotation angle 0
1e-5 m³ (by default).

Humid air volume at shaft rotation angle equal to 0.

Cross-sectional area at port A - area normal to the flow cross-section at the inlet to the transmitter
0.01 m² (by default)

The cross-sectional area of the converter inlet port in the direction normal to the wet air flow path.

Environment pressure specification - method of setting the ambient pressure
Atmospheric pressure (by default)| Specified pressure.

Select the way of specifying the ambient pressure:

Atmospheric pressure - atmospheric pressure is used.

Specified pressure - set the value using the Environment pressure parameter.

Environment pressure - pressure outside the transmitter
0.101325 MPa (by default).

Pressure outside the converter acting against the pressure of the moist volume of air in the converter. A value of 0 means that the gas in the converter is expanding into a vacuum.

Dependencies

Used when Environment pressure specification is set to Specified pressure.

Relative humidity at saturation - relative humidity above which condensation occurs
1.0 (By default).

Relative humidity above which condensation occurs.

Condensation time constant - condensation time constant
1e-3 c (By default).

A time scaling factor characterising the time period for the return of an oversaturated volume of humid air to saturation level due to condensation of excess moisture.

Moisture and trace gas source - moisture and trace gas source
None (By default) | Constant | Controlled

This parameter controls the use of the S port and provides the following options for modelling moisture and trace gas levels within the unit:

None - no impurity gas is introduced into or extracted from the block. The S port is hidden. This value is used by default.
Constant - moisture and impurity gas are introduced into or extracted from the block at a constant rate. The same parameters as in the Moisture Source (MA) and Trace Gas Source (MA) blocks are made available in the block settings. The S port is hidden.
`Controlled' - Moisture and impurity gas are introduced into or removed from the block at a time-varying rate. Port S is open. The Controlled Moisture Source (MA) and Controlled Trace Gas Source (MA) units are connected to this port.

Moisture added or removed - add or remove moisture in the form of water vapour or water
Vapor (By default) | Liquid.

Select whether the unit adds or removes moisture as water vapour or water:

Vapor - the enthalpy of added or removed moisture corresponds to the enthalpy of water vapour, which is greater than the enthalpy of water.
`Liquid' - the enthalpy of moisture added or removed corresponds to the enthalpy of water, which is less than the enthalpy of water vapour.

Dependencies

Used when Moisture and trace gas source is set to `Constant'.

Rate of added moisture - constant mass flow rate through the source
0 (By default).

Mass flow rate of moisture through the source.

A positive value adds moisture to the connected humid air network. A negative value removes moisture from this network.

Dependencies

Used when Moisture and trace gas source is set to `Constant'.

Added moisture temperature specification - moisture temperature specification method
Atmospheric temperature (by default) | Specified temperature.

Selects the moisture temperature specification method:

`Atmospheric temperature' - uses the atmospheric temperature set by the Moist Air Properties (MA) unit connected to the loop.
Specified temperature - the value is set using the Temperature of added moisture parameter.

Dependencies

It is used if the Moisture and trace gas source parameter is set to Constant.

Temperature of added moisture - moisture temperature
`293.15 K (by default).

Enter the desired moisture temperature. This temperature remains constant during the simulation. The unit uses this value only to estimate the specific enthalpy of added moisture. The specific enthalpy of removed moisture is determined based on the temperature of the connected humid air network.

Dependencies

Used when Added moisture temperature specification is set to Specified temperature.

Rate of added trace gas - constant mass flow rate through the source
0 kg/s (By default).

Reflects the mass flow rate of added trace gas through the source. A positive value adds impurity gas to the connected humid air volume, a negative value removes it.

Dependencies

Used when Moisture and trace gas source is set to `Constant'.

Added trace gas temperature specification - method of setting the trace gas temperature specification
Atmospheric temperature (by default) | Specified temperature.

Selects the impurity gas temperature specification method:

`Atmospheric temperature' - uses the atmospheric temperature set by the Moist Air Properties (MA) block connected to the loop.
`Specified temperature' - the value is set using the Temperature of added trace gas parameter.

Dependencies

It is used if the Moisture and trace gas source parameter is set to Constant.

Temperature of added trace gas - temperature of added trace gas
`293.15 K (by default).

Enter the desired temperature of the added trace gas. This temperature remains constant during the simulation. The block uses this value only to estimate the specific enthalpy of the added impurity gas. The specific enthalpy of the removed impurity gas is determined based on the temperature of the connected wet air volume.

Dependencies

Used when the Added trace gas temperature specification is set to Specified temperature.